58 ideas
19335 | Reasonings have a natural ordering in God's understanding, but only a temporal order in ours [Leibniz] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
1564 | True and false statements can use exactly the same words [Anon (Diss)] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
1559 | Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)] |
1561 | Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)] |
1560 | Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)] |
19367 | Saying we must will whatever we decide to will leads to an infinite regress [Leibniz] |
19351 | Perfections of soul subordinate the body, but imperfections of soul submit to the body [Leibniz] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
19331 | Will is an inclination to pursue something good [Leibniz] |
1567 | How could someone who knows everything fail to act correctly? [Anon (Diss)] |
1563 | Every apparent crime can be right in certain circumstances [Anon (Diss), by PG] |
19346 | Most people facing death would happily re-live a similar life, with just a bit of variety [Leibniz] |
19340 | Metaphysical evil is imperfection; physical evil is suffering; moral evil is sin [Leibniz] |
19366 | You can't assess moral actions without referring to the qualities of character that produce them [Leibniz] |
1562 | It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)] |
1566 | The first priority in elections is to vote for people who support democracy [Anon (Diss)] |
1565 | We learn language, and we don't know who teaches us it [Anon (Diss)] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
19326 | God must be intelligible, to select the actual world from the possibilities [Leibniz] |
19327 | The intelligent cause must be unique and all-perfect, to handle all the interconnected possibilities [Leibniz] |
19344 | God prefers men to lions, but might not exterminate lions to save one man [Leibniz] |
19330 | If justice is arbitrary, or fixed but not observed, or not human justice, this undermines God [Leibniz] |
19325 | God is the first reason of things; our experiences are contingent, and contain no necessity [Leibniz] |
19329 | The laws of physics are wonderful evidence of an intelligent and free being [Leibniz] |
19437 | Prayers are useful, because God foresaw them in his great plan [Leibniz] |
19337 | How can an all-good, wise and powerful being allow evil, sin and apparent injustice? [Leibniz] |
19345 | Being confident of God's goodness, we disregard the apparent local evils in the visible world [Leibniz] |